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URL: https://oeis.org/A355196

⇱ A355196 - OEIS

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A355196
Sum of the largest parts of the partitions of n into exactly 3 prime parts.
4
0, 0, 0, 0, 0, 0, 2, 3, 3, 8, 5, 12, 12, 12, 7, 23, 18, 38, 24, 31, 24, 59, 30, 73, 47, 71, 49, 113, 55, 115, 40, 102, 59, 171, 48, 168, 100, 191, 102, 220, 50, 265, 89, 246, 120, 322, 109, 383, 136, 348, 181, 477, 158, 516, 117, 468, 199, 605, 133, 574, 170, 600, 252, 751, 133
OFFSET
0,7
FORMULA
a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} c(i) * c(j) * c(n-i-j) * (n-i-j), where c = A010051.
a(n) = A355199(n) - A355197(n) - A355198(n).
EXAMPLE
a(9) = 8; since 9 can be written as the sum of 3 primes in two ways: 2+2+5 = 3+3+3 and the sum of the largest parts of these partitions is 5+3 = 8, we have a(9) = 8.
MATHEMATICA
Table[Sum[Sum[(n - i - j) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[j] - PrimePi[j - 1]) (PrimePi[n - i - j] - PrimePi[n - i - j - 1]), {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 80}]
Table[Total[Select[IntegerPartitions[n, {3}], AllTrue[#, PrimeQ]&][[;; , 1]]], {n, 0, 70}] (* Harvey P. Dale, Aug 24 2025 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 23 2022
STATUS
approved